at what Year the said Number is reduced to half by Mortality ; and that is the Age , to which it is an even Wager, that a Person of the Age proposed shall arrive before he die . As for Instance; A Person of 30 Years of Age is proposed, the number of that Age is 531, the half thereof is 265, which number I find to be between 57 and 58 Years; so that a Man of 30 may reasonably expect to live between 27 and 28 Years.
Use IV. By what has been said, the Price of Insurance upon Lives ought to be regulated, and the difference is discovered between the
Price of insuring the Life of a Man of 20 and 50. For Example; It being 100 to 1, that a Man of 20 dies not in a Year, and but 38 to 1, for a Man of 50 Years of Age.
Use V. On this depends the Valuation of Annuities upon Lives; for it is plain, that the Purchaser ought to pay for only such a part of the Value of the Annuity, as he has Chances that he is living; and this ought to be computed yearly, and the Sum of all those yearly Values being added together, will amount to the Value of the Annuity for the Life of the Person proposed. Now the present Value of Money payable after a Term of Years, at any given Rate of Interest, either may be had from Tables already computed; or almost as compendiously, by the Table of Logarithms: For the Arithmetical Complement of the Logarithm of Unity, and its yearly Interest, (that is, of 1,06 for Six per Cent. being 9,974694.) being multiplied by the number of Years proposed, gives the present Value of One Pound payable after the end of so many Years. Then by the foregoing Proposition, it will be as the number of Persons living after that Term of Years, to the number dead; so are the Odds that any one Person